# The surface areas of two similar solids are 416yd ^2 and 1,354yd ^2. The volume of the larger solid is 2,976 yd^3. What is the volume of the smaller solid?

2,976 yd ^3
2,619 yd ^3
914 yd ^3
507 yd ^2

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1. The areas of similar objects are proportional to the square of their sides
so 416/1354 = x^2/y^2 , where x and y are corresponding sides , x as the smaller
x^2/y^2 = 416/1354 = 208/677
x/y = √208/√677

the volumes of similar objects are proportional to the cubes of their corresponding sides
x^3/y^3 = volume/2976
(√208)^3 / (√677)^3 = volume/2976
volume = appr 506.8 yds^3